Solution:
The risk neutral probability is given by:
Qu = (e^rt - d) / (u-d) . . . . . .Equation A)
Where Qu -> risk neutral probability of an upmove
r -> risk free rate , t -> period , u -> size of the upmove , d -> size of the downmove
We have with us:
r = 3% (.03) u =115% (1.15) d=90% (.9) t =1 year
Putting the above values in Equation A) we get,
Qu = (e^(.03*1) - .9)/(1.15 - .9)
= (1.0304545 - .9)/(1.15 - .9)
= .130454534 / .25
=.521818136 = 52.1818136 %
The risk neutral probability of an upmove is 52.1818136% and probability of a downmove is (1-Qu) i.e.
1- .521818136 = .478181864
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